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Simplifying 20d2 + -31d + 9 = -3 Reorder the terms: 9 + -31d + 20d2 = -3 Solving 9 + -31d + 20d2 = -3 Solving for variable 'd'. Reorder the terms: 9 + 3 + -31d + 20d2 = -3 + 3 Combine like terms: 9 + 3 = 12 12 + -31d + 20d2 = -3 + 3 Combine like terms: -3 + 3 = 0 12 + -31d + 20d2 = 0 Factor a trinomial. (3 + -4d)(4 + -5d) = 0Subproblem 1
Set the factor '(3 + -4d)' equal to zero and attempt to solve: Simplifying 3 + -4d = 0 Solving 3 + -4d = 0 Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4d = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4d = 0 + -3 -4d = 0 + -3 Combine like terms: 0 + -3 = -3 -4d = -3 Divide each side by '-4'. d = 0.75 Simplifying d = 0.75Subproblem 2
Set the factor '(4 + -5d)' equal to zero and attempt to solve: Simplifying 4 + -5d = 0 Solving 4 + -5d = 0 Move all terms containing d to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5d = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5d = 0 + -4 -5d = 0 + -4 Combine like terms: 0 + -4 = -4 -5d = -4 Divide each side by '-5'. d = 0.8 Simplifying d = 0.8Solution
d = {0.75, 0.8}
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